Question

Given z1 and z2 below. Calculate z1/z2 and write your answer in rcistheta form.

z1=-3+3sqrt(3)i
z2=27i

Answer 1

(2/9)cis(30°)

Explanation:

We can express the two numbers in magnitude∠angle form, then find their ratio.

|z1| = 3√((-1)² +(√3)²) = 3√4 = 6

∠z1 = arctan((3√3)/(-3)) = -arctan(√3) = 120°

z2 = 27∠90°

So, the ratio is ...

z1/z2 = (6∠120°)/(27∠90°) = (6/27)∠(120°-90°)

z1/z2 = (2/9)∠30°